6.F.29 and every other published movement case now passes -- 137 of the 137 that can be run, and 176 of 176 across all four sections. The resolver guesses, and a guess is only ever tested against the guesses in force beside it. Where several cycles are knotted together that is not enough: two readings can each be locally consistent, and the search lands on whichever one the order it happened to start from leads to. 6.F.28 and 6.F.29 are the same ring of six convoy paradoxes with one support between them, and the document keeps the pair to show that the answer swings on it. The document is explicit that there is no straightforward way to fix this inside the recursion. So it is fixed outside it. The resolution is run again, starting each order from the answer the last run gave it rather than from a fresh guess of false. A reading that is genuinely settled reproduces itself and we stop; one that was an artefact of where the search began does not, and the next run starts from somewhere better. Four passes, and a position still arguing with itself after that is oscillating rather than converging, so the first answer stands. Two other corrections came from the document's own text on the way here. Its published resolver replaces "did the dependency list grow" with a guess_based flag saved and restored around every frame, and counts recursion_hits to decide which order a cycle hangs from -- both because the simpler tests stop meaning what they say once more than one cycle exists. And section 5.D's hack: a convoy asks the units attacking it by adjudicating them directly rather than through the resolver, which keeps the dependency graph a set of clean single cycles. Pandin's paradox is the small example -- routed through resolve, the English Channel comes to depend on Wales and Belgium, neither of which is a decision the paradox turns on. The document's test for the head of a cycle still needed one addition: an order named in the cycle that is still on the stack is one of its callers, and while a caller is waiting the answer is that caller's to settle. settle.test.ts checks the property directly rather than through the published cases. An adjudicator that cannot reproduce its own answer is not finished, whatever it scores.
436 lines
22 KiB
Markdown
436 lines
22 KiB
Markdown
# Great Powers
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A browser rebuild of the classic seven-power negotiation game: one human
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against six computer powers, in one sitting.
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Not the name you expect, and [NOTICE.md](NOTICE.md) will make the argument at
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length once there is more to notice. The short version is the one the
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starship game already made on this site: the rules are free to rebuild, the
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trademark and the published artwork are not. "Great Powers" is what those
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seven were called at the time.
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## What this is, and what it is not
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**One human, six computer powers, one sitting.** The original is seven people
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over weeks. A hub with no traffic cannot deliver that, and nobody is going to
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wait months for six strangers — so the other six are played by the machine
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and a game is finished in an evening.
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**It still has to be a negotiation game.** A version where you simply write
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orders is a good movement puzzle and not this game. So:
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- **Both sides open.** Bots approach you with proposals; you approach them.
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Neither waits for the other.
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- **On real terms.** Offers are concrete and about this turn or the next few
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— support this move, keep out of that province, no attack until 1903 — and
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are accepted or refused on their merits, not by a die roll.
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- **Betrayal is a move, not a bug.** A bot can agree to support you and then
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not do it, and so can you. Bots remember who kept their word, tell each
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other, and price you accordingly. That is the game.
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The press is **structured rather than free text**: typed offers, deterministic
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reasoning, and no model anywhere in it. That makes betrayal auditable — you
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can read exactly why a power turned on you — and testable, which free text
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would not be.
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## The look and the sound
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**The map is the standard board's geometry, under the same licence as this
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project.** The outlines come from the diplomacy engine at
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<https://github.com/diplomacy/diplomacy>, which is AGPL-3.0, extracted by
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`tools/map.py` into `src/game/board.json`. Every colour and every mark drawn
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on it is ours; see [NOTICE.md](NOTICE.md).
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Three earlier attempts drew it from scratch and all three were worse.
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Dividing the plane by nearest province gives a tidy board that looks nothing
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like Europe. Drawing the adjacency graph gives something unimpeachable about
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the rules and not a map at all -- circles joined by lines. Fifty-six polygons
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placed by eye gives fifty-six islands. Drawing Europe accurately is real work,
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somebody did it properly, and they published it under a licence that invites
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exactly this.
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**Clicking still answers with the rules, not the picture.** A shape cannot say
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that a fleet on Spain's north coast may not enter the Gulf of Lyon while one
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on the south coast may, because both coasts are the same shape. So selecting a
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province lights up exactly where its unit may legally go, taken from the
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adjacency graph.
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**It gets the whole screen.** The other three games live in a four-by-three
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cabinet because the machines they are rebuilding did. This one is not
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rebuilding a machine, and seventy-five provinces plus somebody trying to talk
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you out of Galicia do not fit in a letterbox. The map takes the viewport.
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**The music is not cartoony, and that is the point.** It is 1914: serious,
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and intense. The joke of this game is that something charming to look at is
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the cruellest thing on the site, and the score is what says so.
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**And the turn should be heard.** Orders resolve in silence in every online
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version of this game, which is a waste of the one moment anybody cares
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about. Armies grinding into each other, guns at sea, a convoy escorting
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something across, a unit being built, a unit falling back -- each of those is
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a different noise, generated by the synth like everything else on this site.
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**The endings get their own.** This game does not end in a win or a loss, it
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ends in one of four things, and they do not sound alike:
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- **the solo** -- eighteen centres, and the only unambiguous victory there is;
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- **elimination** -- your last centre gone, which can happen in 1903 and
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leaves you watching;
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- **the draw** -- nobody reaches eighteen and the survivors agree to stop.
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This is what actually happens most of the time, and it is neither a win nor
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a loss, so it cannot borrow either of their tunes;
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- **somebody else's solo** -- you are still on the board and it is over
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anyway, which is the bleakest of the four and should sound like it.
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## The board
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Seventy-five provinces, two adjacency graphs — an army walks the land, a
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fleet follows the water — and three provinces with two coasts that do not
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connect, where a fleet has to say which one it is on.
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The topology is a fact about a published game and free to use. The artwork is
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not, and there is none here: the map this game draws is generated from the
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data, the way the cave game's dodecahedron is.
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`npm test` checks the board against itself. The one that earns its keep is
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symmetry: an adjacency list this size is typed by hand once and wrong in
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three places unless something looks. It found the Skagerrak wired to the
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Baltic on the first run — which would have quietly opened a back door into
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the Baltic and made Denmark worthless.
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## The published test cases
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`tools/datc.py` turns the Diplomacy Adjudicator Test Cases into
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`src/game/datc.json` -- the orders and their annotated outcomes, not the
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document's prose, which is Lucas Kruijswijk's writing. Every one of the 176
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published cases is parsed and run.
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| Section | | Passing |
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| --- | --- | --- |
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| 6.A - 6.G | movement | 137 / 137 |
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| 6.H | retreating | 18 / 18 |
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| 6.I | building | 7 / 7 |
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| 6.J | civil disorder | 13 / 13 |
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All 176 pass.
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They are the reason this adjudicator is worth trusting: they found that
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orders were never validated, that the paradox rule did not terminate, that
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civil disorder was measuring the wrong distance, and that five of my own
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hand-written cases rested on a support Paris cannot give.
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Three of the hundred and forty movement cases are excluded rather than
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failed. 6.A.6, 6.B.10 and 6.B.11 state their setup in prose -- "Germany has
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a fleet in London" -- and the fixture is built from order lines, so it
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cannot carry a unit nobody ordered. The other hundred and thirty-seven all
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pass.
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There are no known deviations left.
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### What the failing cases were worth
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They found six real faults, which is the whole argument for running somebody
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else's tests rather than only your own. Every one of them was invisible in
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play: the engine had an answer, the answer looked reasonable, and it was
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wrong.
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**The illegal/invalid line (6.A.5, 6.D.8).** The document separates an order
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that is impossible *in this position* from one this position allows that
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merely did not come off. The first is ignored and the unit is holding like
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any other; the second means the unit tried to leave and cannot be propped up
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where it stands. An army sent across water with a fleet on the route and no
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convoy ordered is the second (6.D.8); the identical order with nobody in the
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sea at all is the first (6.D.32). Guessing at this once cost four passing
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cases to buy one. Reading it properly cost nothing.
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**A support that only looked like a hold (6.A.5).** "Supports A Yorkshire"
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and "Supports A Yorkshire - Yorkshire" are the same shape once parsed, and
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the case turns on the difference: the first holds a unit down, the second
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supports a move nobody can legally make. The extractor now keeps the
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distinction; it was losing it.
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**The head of a cycle (6.F.22, 6.F.28).** Kruijswijk's resolver guesses that
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an order fails, sees what follows, and guesses the other way. Only the
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*outermost* order in a cycle may do that, because its answer is the one
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everything else was computed against. This engine let any order that reached
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the dependency list first declare the cycle its own -- and an inner one
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takes both guesses with its callers' provisional answers held fixed, gets
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the same result twice for that reason, and records it as settled. The cycle
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then becomes invisible: the backup rule never runs, and the position
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resolves to whichever of its two consistent readings the search walked into
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first. It had been doing that on every paradox and getting away with it,
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because on a first-order paradox both readings agree.
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Fixing it took two passes. The first asked only whether the cycle had come
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back round to this order, which fixed 6.F.22. 6.F.28 needed the second: an
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order may not settle a cycle while *any* entry in the dependency list is
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still waiting further down the stack, not merely the entries added since it
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started. Six paradoxes in a ring, each a tidy four-order cycle in its own
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right, and each was settling itself locally against a caller's provisional
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answer. The ring they were links in was never seen at all.
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**The answer has to agree with itself (6.F.29).** The resolver guesses, and
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a guess is only ever tested against the guesses in force beside it. Where
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several cycles are knotted together that is not enough: two readings can
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each be locally consistent, and the search lands on whichever one its
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starting order leads to. The document is explicit that there is no
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straightforward way to fix this inside the recursion -- so it is fixed
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outside it. The resolution is run again, starting each order from the answer
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the last run gave it. A reading that is genuinely settled reproduces itself;
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one that was an artefact of where the search began does not, and the next
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run starts from somewhere better. Four passes, and a position still arguing
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with itself after that is oscillating rather than converging, so the first
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answer stands.
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**A superfluous convoy order (6.G.19).** For a convoy order the fleet has to
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be necessary to some route -- there must be a route, ordered or not, that
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needs it. The path finder now considers only *proper* routes, which never
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jump to a province an earlier fleet in the chain already reached: Tunis -
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Ionian - Adriatic - Albania is not one, because the Ionian touches Albania
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and the Adriatic is doing nothing. It decides whether two units swap places
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or bounce off each other, and the document's own advice is that an
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interactive system should never offer the order.
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Sections H, I and J -- retreating and the winter -- have engine code but no
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harness yet; their cases are shaped differently and need one.
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## The bots
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`src/game/evaluate.ts` prices a position and `src/game/bot.ts` plays it.
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Everything a power does comes out of two numbers, and they are deliberately
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few: when a power turns on you, you are entitled to know what it thought it
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was getting and be furious about the price rather than confused by it.
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`chooseOrders` returns its reasoning as a list of sentences for exactly that.
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Centres are the only thing that counts. Units are how you get them and are
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worth nothing in themselves -- a power with eight units and four centres is
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losing, and will have four units by the winter.
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Two things the tests had to teach it. It garrisons a threatened centre it is
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already standing on, because scoring only *moves* had it defending Berlin by
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marching the Munich garrison there -- abandoning one centre to save another
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of identical value. And it never shoves at its own countryman, which has no
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strength at all and is two units wasting a turn on each other.
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The price of breaking a promise is **how far this power trusts the partner**,
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not how far the partner trusts it. Pricing it the other way round gives a
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power that has been lied to four times a high cost of retaliating, because it
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has been scrupulous itself and is still well thought of, which is exactly
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backwards. An ally who has already betrayed you is worth nothing to protect.
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Bots open negotiations rather than only answering them. `propose()` works
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from the plan the power has already made: it decides what it wants to do this
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turn, notices where that will not work alone, and goes looking for somebody
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who could make it work. Help taking something defended, first; then a quiet
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border over ground neither of them owns; then peace outright, when a
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neighbour is over your centres and your ambitions are elsewhere. Three
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approaches a turn at most, because six powers all talking at once is a
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mailstorm rather than a negotiation.
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Each overture carries what the power actually says, so it can be put in front
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of a human as a message rather than as a form.
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**A power will offer a quiet border to somebody it is attacking somewhere
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else**, and that is deliberate. Germany marching on French Belgium while
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suggesting both sides leave Burgundy alone is not a lie and not incoherent: a
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promise about Burgundy is a promise about Burgundy, and it will be kept to
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the letter by somebody who is robbing you at the same moment. A bot that
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refused to make that offer would be playing a politer game than this one. It
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will not, however, ask the power it is attacking to *help*, or offer it peace
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while the orders say otherwise.
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## Giving orders
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Clicks on the board, because that is where the question is. Select a unit,
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pick a verb, and the provinces the next click will accept light up -- so
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nobody writes a move the rules were never going to allow, and nobody has to
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learn a notation to find that out.
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Everything offered comes from the rules rather than from the map, which is
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the same split the map itself is built on. A fleet on the north coast of
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Spain is drawn identically to one on the south coast and can go to entirely
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different places; no shape can express that, and the highlight has to.
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Orders are drawn where they are given: an arrow to where a unit is going, a
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dashed line to what a support is holding up, a ring round a unit that is
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staying. The list beside the board says the same thing in the rules' own
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words, because an arrow cannot tell you that the support you meant for Vienna
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is being given to Budapest. Anything the rules will not take is struck
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through in the list as it is written, rather than after the turn.
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## The turn
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`src/game/game.ts` is the loop, and it has no interface attached on purpose:
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a whole game can be played out in a test from the opening to whatever end it
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finds. That is the only way to answer the question that actually matters
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about the bots -- not whether each order looks sensible, but whether seven
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powers left alone reach a conclusion.
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Spring orders, retreats, autumn orders, retreats, then the winter, which is
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the only phase that changes who owns anything.
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Before the orders, everybody talks. Computer powers approach each other,
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answer on the merits, and what they agree binds that turn and is judged at
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the end of it. Approaches to the human are handed back rather than answered
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for them.
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**The game is called at the end of 1912.** Diplomacy has no clock of its own:
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it ends on eighteen centres, or when the players agree to stop -- and
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agreeing to stop is a conversation seven computer powers are never going to
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have. Left alone they reach a standoff and hold it, which is what a table of
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equally cautious players does and is why real games are called.
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So: eighteen centres wins outright, and if nobody has them by the end of 1912
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the survivors draw. Twelve years is a long evening and a real tournament
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length, and **the draw is a proper ending here rather than a failure to
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finish** -- it is the commonest way this game actually ends.
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Worth saying plainly: seven bots left alone draw. They take centres off each
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other now, which they could not do at all before, but none of them breaks
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away to a solo. Beating six of them is the game.
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## The other two phases
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A beaten unit that finds somewhere to stand is a nuisance for years; one that
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does not is gone. And the winter is where a good spring turns into a bigger
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army, or does not. Both are decisions, and both were being taken *for* the
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player while the rest of this was built, which quietly removed half the
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consequence of the turn they had just played.
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They are offered as places rather than as a notation, for the same reason the
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orders are: the rules already know what is allowed, so the interface only
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ever offers what is. A beaten unit lists the provinces it may fall back to and
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nothing else; the winter lists the home centres that are yours and empty, with
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a fleet offered only where a fleet could sit.
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The game steps past anything with no decision in it. A retreat phase where
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none of your units was thrown out, or a winter where your centres and units
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are level, is not a choice -- it is a screen asking you to press Done.
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## Writing a support
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Support is the order the whole game turns on, and it was the order this
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interface was worst at taking.
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The rule is that the supporting unit must be able to reach the province the
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supported unit is *going to* -- not the province it is standing in. The board
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was offering the wrong set: only units standing next door. So Vienna could
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not support Venice into Tyrolia, which is a perfectly ordinary order --
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Vienna and Tyrolia touch, Vienna and Venice do not -- and there was no way
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to say it. It also offered support to hold for units too far away to prop
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up, wrote the order anyway, and let the adjudicator quietly turn it into a
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hold after the turn was submitted.
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That question now lives in `src/game/targets.ts` with the rest of the rules,
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where it is eight tests rather than a closure in a component.
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The second half was that a stray click threw away a half-written order. You
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picked Support, picked the unit to help, missed the destination by a
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province, and the whole thing silently became a fresh move somewhere else.
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A two-part order now stands its ground and says no; clicking the unit giving
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the order takes you back to the start of it. And the unit you picked to
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support is marked on the board in a different colour from the unit giving
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the order, because otherwise the second half is written blind.
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## Ordering a convoy
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The rules have had convoys all along -- fifty of the DATC cases are about
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them, including the paradoxes -- but for a while you could not order one.
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The board offered an army the provinces it could walk to, and a crossing is
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by definition not one of those, so the army's half of a convoy could not be
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written. The fleet's half could, which made it worse: the verb was there and
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did nothing anybody could use.
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An army on a coast is now also offered the coasts a chain of crewed seas can
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reach, drawn in blue and with long dashes so a crossing does not look like a
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march. A sea counts if there is a fleet standing in it, whoever owns it. A
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fleet that has not been ordered to convoy still counts: it is a thing that
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could be arranged, which is what the negotiation is for, and the adjudicator
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will bounce the crossing if it was not.
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That is deliberately not the question the rules ask when they *judge* a
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convoy, which is whether water could ever get there. That one says yes to
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most of Europe. Offering thirty provinces because a chain of fleets is
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conceivable would be worse than offering none.
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Clicking a blue coast writes the move `viaConvoy`, which is not a formality:
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the rules allow a unit to be convoyed to a province it could have walked to,
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and the two orders resolve differently.
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The two halves are written separately, as they always have been, and the
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order list says so while only one of them exists -- `A Yorkshire → Norway`
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sits there in red until `F North Sea convoys Yorkshire → Norway` joins it,
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and then both go black. Nothing was added to make that happen. The validator
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already knew.
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### Half a convoy
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Multi-fleet convoys work -- London to Spain across the Channel and the
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Mid-Atlantic, with both fleets ordered to carry -- and the DATC's fifty
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convoy cases say so. What did not work was finding that out.
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A convoy takes as many orders as there are seas to cross, and the rules give
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two different answers to writing fewer. No fleet ordered at all and the move
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is *illegal*: legality is decided on the board alone, so the panel reddens
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it. One fleet of a two-fleet chain and the move is perfectly *legal*. It
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simply fails, silently, a turn later, with nothing on screen to distinguish
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it from having been blocked.
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From the chair where the orders are written those are the same complaint --
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nobody is carrying this. And it is worse than it looks, because the board
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deliberately offers crossings that run through other powers' fleets, which
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cannot be ordered at all, only asked for. So the panel now answers the one
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question that matters: given everything on the table, is there a chain that
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gets this army there? If not it says which is missing -- *no fleet has been
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ordered to carry it*, or *ordered to carry it, but not the whole way*.
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## Before the map, and how to stop
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A landing page, because Diplomacy has a reputation and about half of it is
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wrong. The rules are short enough to state completely and strange enough
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that stating them is a courtesy: there is no luck in this game at all, every
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unit is exactly as strong as every other, and nothing happens on the board
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that somebody did not agree to help with. It is also the honest place for
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the licence and for where the map came from -- a page that says nothing
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about that is a page quietly hoping nobody asks.
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The dice that play when you start are the only joke in here. There are no
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dice in Diplomacy; that is the sound of every other board game you have
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|
played, and the last one you hear before finding out that none of this is
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|
luck.
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Giving up is two different things and `src/game/concede.ts` keeps them
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apart.
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**Resigning is unilateral.** Nobody is entitled to your attention, so nobody
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|
votes on it. But your power does not leave the board: it goes into civil
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|
disorder, holds everything, waives its builds and is paid off as it loses
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|
centres, which is what the rules already say happens to an absent player.
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|
That matters to everybody else. A resigned Austria is still eleven centres
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|
somebody has to go and take, and letting them evaporate would hand the game
|
|
to whoever happened to be next door.
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|
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|
**A draw is not unilateral**, and that is the part that keeps it Diplomacy
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|
rather than a menu. Every surviving power votes and one refusal is enough,
|
|
because being able to end the game by asking would be worth more than any
|
|
alliance in it. A power refuses while it leads or is within two centres of
|
|
leading, and it says so: *"England is 1 behind and thinks that is
|
|
catchable."* Asked in Spring 1901 every one of the other six refuses, which
|
|
is the right answer -- a game that could be drawn on the first turn would
|
|
not be worth playing.
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|
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|
**Conceding** -- handing the game to whoever is winning -- is harder to get
|
|
than a draw, and it should be. It only carries when the solo was coming
|
|
anyway: the leader is within four of eighteen and nobody left can close the
|
|
gap. Otherwise refusing costs nothing but time, and time is the only thing
|
|
the losing side has.
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|
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|
Elimination is the third way out and needs no button. When your last centre
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|
goes you are told so and the rest plays out; you can watch it or close the
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|
tab, and either way the board is still worth seeing.
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|
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|
## Still to build
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|
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|
- bots strong enough to solo against each other, not only to draw
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|
- the music, the battle sound, the four endings
|